Optical transmission, in which an information signal is modulated onto an optical carrier, is widely employed in modern communications systems. In particular, wide-area communications networks employ long-haul transmission links using single mode optical fibres for the transmission of digital information at very high bit rates, using one or more optical carriers, or wavelengths, over each fibre. The distance over which data may be transmitted in single mode optical fibres before some form of regeneration is required may be limited by optical attenuation, accumulated noise (eg from optical amplifiers), linear dispersion mechanisms, such as chromatic dispersion (CD) and polarisation mode dispersion (PMD), and non-linear processes, such as self phase modulation (SPM).
Recently, there has been considerable interest in coherent optical transmission technique, including coherent optical QPSK (CO-QPSK) and coherent optical OFDM (CO-OFDM) for next-generation long-haul transmission systems operating at bit rates of 100 gigabits per second or higher. Both of the aforementioned coherent optical modulation technologies may be employed to compensate for linear impairments such as CD and PMD, and thus fibre non-linearity is a significant limiting factor of transmission distance in such systems.
It is known that the linear and non-linear signal distortions may be completely reversed (in the absence of random noise processes) by propagating the distorted signal through a transmission span having characteristics that are precisely the inverse of the main transmission span. While such an “inverse span” does not exist in reality, it may be simulated using computational techniques applied to an inverse fibre model. Propagation through the inverse fibre model may be computed either at the transmitting end (in which case a pre-distorted signal is transmitted and the pre-distortion reversed in the transmission link) or at the receiver (in which case a distorted signal is detected, and propagation through the inverse model is simulated in order to recover the transmitted signal). The process of simulated propagation through an inverse model is referred to herein as “backpropagation”.
While the backpropagation technique has been shown to be highly effective in mitigating the effects of both linear and non-linear distortion, it has the disadvantage of being highly computationally intensive. In particular, accurate backpropagation computation requires solution of the inverse non-linear Schrödinger Equation (NLSE), which governs the dispersive and non-linear propagation of the signal through the fibre link. Typically, the NLSE is solved numerically using the split-step Fourier method (SSFM), in which the fibre link is divided into a sequence of shorter segments, and propagation through each segment is simulated by computing separately the linear propagation, in the frequency domain, and the non-linear propagation, in the time domain. Thus each step involves two Fourier transforms, along with the multiplications required to implement the linear and non-linear phase shifts of the signal. Generally higher accuracy is achieved by using a smaller step size (ie segment length), and techniques are available to estimate the required step size in order to achieve a given level of desired accuracy.
In practice, it has been shown that for an optical transmission link comprising a plurality of fibre spans interconnected via optical amplifiers configured to compensate for transmission losses within each span, the step size for the split step method may be increased up to the span length with an acceptably small reduction in accuracy. This is because the effect of non-linear processes is essentially confined to the input end of each fibre span, at which the optical power is greatest. However, further reductions in the number of steps will result in significant loss of accuracy. Furthermore, digital computation of non-linear backpropagation requires at least three times oversampling of the signal, because the major non-linear effects in optical fibre transmission are of third order. Accordingly, it has been determined that the implementation of a backpropagation compensator for a transmission link including only 25 spans requires over 100 times the computational power of that required for linear equalisation only.
Accordingly, there is a need for computational methods, and corresponding apparatus, that are able to perform linear and non-linear equalisation of optical signals transmitted over long multi-span transmission links that requires significantly reduced computational resources compared to prior art techniques.